65/19 atom

Interval information

Ratio	272629760/272629233
Factorization	222 × 3-15 × 5 × 13 × 19-1
Monzo	[22 -15 1 0 0 1 0 -1⟩
Size in cents	0.003346521¢
Name	65/19 atom
Color name	ss19u3oy2, sasa-nuthoyo 2nd
FJS name	[math]\text{d2}^{5,13}_{19}[/math]
Special properties	reduced
Tenney height (log2 nd)	56.0447
Weil height (log2 max(n, d))	56.0447
Wilson height (sopfr(nd))	126
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.19982 bits
Comma size	unnoticeable
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272629760/272629233, the 65/19 atom, is a 19-limit (2.3.5.13.19 subgroup) unnoticeable comma. It represents the tiny interval between the pythagorean comma 3¹²/2¹⁹ and the wilsorma 65/64 lowered by the 19-schisma 513/512.

Notably, the 65/19 atom is also the amount by which the 13-comma 6656/6561 ("tetris comma") exceeds the 19/5-comma 41553/40960 (an apotome above 19/16 lowered by 5/4). Their difference is small enough that the untempered Promethian (high precision) and Herculean (ultra precision) sagittal accidental systems equate the 13-comma with the 19/5 comma: the most accurate possible representation of the 13th harmonic in JI sagittal accidentals at these precision levels (as three octaves above a ⁠ ⁠P5) accrues this 0.0033¢ error.